悬链线精确状态方程的解法

Solving process of exact state equation for catenary

在目前的设计工作中,架空电线状态方程的形式及其解法虽有多种,但都是在抛物线基础上简化的,设计计算时会存在一定的误差,而在大高差、大档距、大风偏时误差较为明显。悬链线精确状态方程是一个包含双曲函数的超越方程,使用牛顿迭代法进行了求解,在求解过程中采用了大档距、大高差、大风偏的悬链线精确状态方程并提供了结果值的验证方法。

Although there are many forms of the state equation for the overhead wire and their solving processes in present design work,they are all simplified based on the parabola.Certain error will occur in design calculation based on these forms of state equation;especially,the error will be more obvious under the conditions of large altitude difference,large span and large windage yaw.The exact state equation for the catenary is transcendental equation including hyperbolic function.Using the Newton iteration method,the solution of the equation was found.In the solving process,the exact state equation for the catenary with conditions of large altitude difference,large span and large windage yaw was adopted,and the result verification method was given.